Our galaxy sample is drawn from the New York University Value Added
Galaxy Catalog (NYU-VAGC) sample [1]}
of the Sloan Digital Sky Survey (SDSS) DR7 [2]}. In this paper,
we mainly focus on central galaxies, which is defined as the most
massive galaxies in galaxy groups. Here, we use the galaxy group
catalog constructed by using the halo-based group-finding
algorithm[3]}, [4]} to separate centrals from satellites.
Following [4]}, we select galaxies with r-band
Petrosian magnitudes \(r\le \)  17.72, with redshifts in the range
\(0.01 \le z \le 0.2\) , and with redshift
completeness \(C_{z} >\)  0.7. Stellar mass of individual
galaxies, \(M_*\) , are obtained using the relation between
the stellar mass-to-light ratio and color, as given by [6]},
but assuming a Kroupa IMF [7]}.
This leads to a \(-0.1\)  dex correction in the stellar mass-to-light
ratios relative to the original values. To obtain the
star formation rate (SFR) and 4000Å break (\(D_n4000\) ) of
individual galaxies, we combine our galaxy sample with the
MPA/JHU SDSS catalog[8]}.
The total galaxy sample (tG) contains 593,227 galaxies, of which
452,177 are identified as centrals (hereafter cG).
